Solve for $x$ and $y$ using elimination. ${3x-4y = -13}$ ${-4x-2y = -34}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${3x-4y = -13}$ $8x+4y = 68$ Add the top and bottom equations together. $11x = 55$ $\dfrac{11x}{{11}} = \dfrac{55}{{11}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {3x-4y = -13}\thinspace$ to find $y$ ${3}{(5)}{ - 4y = -13}$ $15-4y = -13$ $15{-15} - 4y = -13{-15}$ $-4y = -28$ $\dfrac{-4y}{{-4}} = \dfrac{-28}{{-4}}$ ${y = 7}$ You can also plug ${x = 5}$ into $\thinspace {-4x-2y = -34}\thinspace$ and get the same answer for $y$ : ${-4}{(5)}{ - 2y = -34}$ ${y = 7}$